In the given optical instrument,how can a thi | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The system consists of two lenses with focal lengths $f = 10 \, cm$ separated by $70 \, cm$. The object is placed $20 \, cm$ in front of the first

Vedclass · Accepted Answer

$20 \, cm$ from the left lens

Vedclass · Answer

(A) The system consists of two lenses with focal lengths $f = 10 \, cm$ separated by $70 \, cm$. The object is placed $20 \, cm$ in front of the first lens.Using the lens formula $\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$ for the first lens:$u = -20 \, cm, f = 10 \, cm$$\frac{1}{v} - \frac{1}{-20} = \frac{1}{10} \implies \frac{1}{v} = \frac{1}{10} - \frac{1}{20} = \frac{1}{20} \implies v = 20 \, cm$.This means the first lens forms an image $20 \, cm$ behind it. This image acts as the object for the second lens.The distance between the lenses is $70 \, cm$,so the distance of this image from the second lens is $70 - 20 = 50 \, cm$.To increase the light-collecting efficiency,we place a third lens of the same focal length $(f = 10 \, cm)$ at the position of the intermediate image ($20 \, cm$ from the first lens). This lens converges the diverging rays from the first lens,preventing them from missing the second lens,without altering the final image position.Thus,the third lens should be placed $20 \, cm$ from the first (left) lens.

In the given optical instrument,how can a third lens of the same focal length be inserted to increase the light-collecting efficiency without changing the positions of the object and the image? Calculate the position of that lens.

Similar Questions

$A$ combination of two thin lenses in contact has a power of $+10 D$. The power reduces to $+6 D$ when the lenses are $0.25 m$ apart. The power of each individual lens is:

$A$ thin convex lens of focal length $30 \, cm$ forms an image $2 \, cm$ high,of an object at infinity. $A$ thin concave lens of focal length $20 \, cm$ is placed $26 \, cm$ from the convex lens on the side of the image. The height of the final image is.....$cm$.

Two thin convex lenses of focal length $f_1$ and $f_2$ are placed in contact with each other. The equivalent power of the lens combination is . . . . . . .

The power of an achromatic convergent lens combination consisting of two lenses is $+ 2D$. The power of the convex lens is $+ 5D$. The ratio of the dispersive power of the convex lens to the concave lens will be:

An achromatic convergent lens of focal length $20 \, cm$ is made of two lenses (in contact) of materials having dispersive powers in the ratio of $1 : 2$ and having focal lengths $f_1$ and $f_2$. Which of the following is true?

Vedclass Test Series

Exam Paper Generator

Online Exam Module